Results 1 to 9 of 9

Math Help - Cocky UPenn student throughs down challenge

  1. #1
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599

    Cocky UPenn student throughs down challenge

    Draw an isosceles triangle ABC with Side AB = Side AC. Draw a line from C to side AB and label that line CD. Now draw a line from B to side AC. Label that line BE. Let angle EBC = 60 degrees, angle BCD equal 70 degrees, angle ABE equal 20 degrees, and angle DCE equal 10 degrees. Now draw line DE.

    Find what angle EDC is by using geometry only and no trigonometry.

    Don't cheat and use protractors/rulers/all that stuff either! Go by pure geometric reasoning
    This is a tedious drawing so if you are going to procede I'll thank you in advance. Here is my reasoning for solving this problem.

    Call the intersection of BE and CD point M. Let ADE=x, EDM=y, DEA=z, and DEM=140-z.

    Thus we have the following system of equations:

    (x+y)+20+10=180
    x+20+z=180
    50+y+(140-z)=180

    And when I solve this I get a large angle, a negative angle, and an angle of zero. I think my work is sound. Please look it over.

    Thanks
    Last edited by Jameson; May 4th 2006 at 06:58 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Try searching the internet for Langley's Problem. It is similar-I solved it some time ago using trigonometry.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Thanks. This is very similar. If you have time though or if someone else does, I'd appreciate it if it would be possible to look over my work. I'll try to include a diagram, but I think I haven't made any errors.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Jameson
    Thanks. This is very similar. If you have time though or if someone else does, I'd appreciate it if it would be possible to look over my work. I'll try to include a diagram, but I think I haven't made any errors.
    Not necessarily you made a mistake, but the determinant of this system is zero. Because the matrix's diagnol is filled with zeros.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Then I need to find a way to set a system with a non-zero determinant. Hmmm... any ideas? I'm only missing four angles on this diagram.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Jameson
    Then I need to find a way to set a system with a non-zero determinant. Hmmm... any ideas? I'm only missing four angles on this diagram.
    This problem is not designed to be treated as a high-school angle solving problem. The trick it to draw a contrusction and even from there it is difficult.
    BTW if your system is consistent, then all solutions can be expressed though a parameter t. Then all you need to to find a solution that is 'reasonable' since there are infinitely many.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Dec 2005
    Posts
    117
    hmm, i'll work on it
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Dec 2005
    Posts
    117
    is it 60????

    EDIT: ok, nevermind that's wrong.
    Last edited by c_323_h; May 9th 2006 at 04:26 PM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    The answer is 20. The question was asked on www.collegeconfidential.com on the UPenn forum, and the OP hasn't posted an explanation to the solution to this problem. Here is a link that will guide you though. http://agutie.homestead.com/files/LangleyProblem.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] How do I become a better student for pre calculus?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 4th 2011, 07:45 PM
  2. Tallest Student
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 2nd 2008, 04:37 AM
  3. Megsss Student
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 15th 2008, 07:31 AM
  4. Megsss Student
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 14th 2008, 03:56 PM
  5. Desperate Student
    Posted in the Calculus Forum
    Replies: 19
    Last Post: April 20th 2008, 10:14 PM

Search Tags


/mathhelpforum @mathhelpforum